Predicting retention data in gas-liquid chromatography by multivariate analysis

Satisfactory reproduction of the retention data matrix in the case of a series of mono-substituted benzenes and a series of aliphatic substances proves the general character of the prediction equation

where x_Qi, φ_j are the retention data x of unknown solute Q_i on phase φ_j; a_Qi, b_Qi, c_Qi and d_Qi are regression coefficients which to some extent account for forces of orientation, charge transfer and association; and x_STi, φ_j are independent variables representing the retention data of the four compounds of the standard set of substances on a given phase φ_j. These four compounds are selected by diverse methods of multivariate analysis. The predicted values show very satisfactory agreement with the observed values.     

Simultaneous mixture analysis by using non-linear spectrophotometric data and linear iterative target transformation factor analysis

Non-linear absorption spectral data obtained from ternary mixtures of analytes are analyzed by using a linear model, iterative target transformation factor analysis (ITTFA). The use of transformed original variables is used to correct non-linearities in the original data. Absorbance below a certain limit (k) is described as linear and above this limit as non-linear. The extension of the regressor variables is the squared absorbances above the linear range. The variation of the prediction error as a function of the number of the factors and the k-values were considered and the minimum prediction error was evaluated for reaching to optimum. Except the natural non-negativity constraint the correlation constraint also is used on concentration vector in each iteration of ITTFA algorithm. The reliability of the method is evaluated using model data for ternary mixtures by spectral overlapping and different degrees of non-linearity. Simultaneous spectrophotometric determination of Eu³⁺, UO₂²⁺ and Th⁴⁺ with arsenazo III as chromogenic reagent is used as experimental model systems with non-linearity behavior of Eu³⁺and UO₂²⁺ components. The application to both synthetic and real data sets with different degrees of non-linearity demonstrate the ability of the proposed methodology to obtain better results than original data and ITTFA. The relative standard errors of prediction for proposed method in comparison with using the PLS calibration on original and extended data are nearly smaller.     

Enhanced target factor analysis

Target testing or target factor analysis, TFA, is a well-established soft analysis method. TFA answers the question whether an independent target test vector measured at the same wavelengths as the collection of spectra in a data matrix can be excluded as the spectrum of one of the components in the system under investigation. Essentially, TFA cannot positively prove that a particular test spectrum is the true spectrum of one of the components, it can, only reject a spectrum. However, TFA will not reject, or in other words TFA will accept, many spectra which cannot be component spectra. Enhanced Target Factor Analysis, ETFA addresses the above problem. Compared with traditional TFA, ETFA results in a significantly narrower range of positive results, i.e. the chance of a false positive test result is dramatically reduced. ETFA is based on feasibility testing as described in Refs. [16–19]. The method has been tested and validated with computer generated and real data sets.     

The thermodynamic dissociation constants of methotrexate by the nonlinear regression and factor analysis of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of methotrexate — chemically (2S)-2-[(4-{[(2,4-diamino-7,8-dihydropteridin-6-yl)methyl] (methyl)amino}phenyl)formamido]pentanedioic acid (the cas number 59-05-2) at various ionic strengths I of range 0.01–0.4, and at temperatures of 25°C and 37°C, were determined with the use of two different multiwavelength and multivariate treatments of spectral data, SPECFIT32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis according to a general rule of first, determining the number of components, and then calculating the spectral responses and concentrations of the components. Concurrently, the experimental determination of the thermodynamic dissociation constants was in agreement with its computational prediction of the PALLAS programme based on knowledge of the chemical structures of the drug. The factor analysis in the INDICES programme predicts the correct number of light-absorbing components when the data quality is high and the instrumental error is known. Three thermodynamic dissociation constants were estimated by nonlinear regression of {pK _a , I} data: for methotrexate pK_a1^T= 2.895(13), pK_a2^T= 4.410(14), pK_a3^T= 5.726(15) at 25°C and pK_a1^T= 3.089(15), pK_a2^T= 4.392(12), pK_a3^T= 5.585(11) at 37°C, where the figure in brackets is the standard deviation in last significant digits. The reliability of the dissociation constants of the drug were proven by conducting goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data.      

Comparison of the target transformation factor analysis of coal composition data with x-ray diffraction analysis

The ability of target transformation factor analysis (t.t.f.a.) to identify and resolve quantitatively the sources of mineral matter inclusion in whole coal samples is described. In order to ascertain the accuracy of these results, the t.t.f.a. values are compared to the relative concentrations of mineral matter phases as determined by x-ray diffraction analysis. Excellent agreement is obtained between the two sets of results.     

Predicting the cross-reactivities of polycyclic aromatic hydrocarbons in ELISA by regression analysis and CoMFA methods

Immunoassays have been regarded as a possible alternative or supplement for measuring polycyclic aromatic hydrocarbons (PAHs) in the environment. Since there are too many potential cross-reactants for PAH immunoassays, it is difficult to determine all the cross-reactivities (CRs) by experimental tests. The relationship between CR and the physical-chemical properties of PAHs and related compounds was investigated using the CR data from a commercial enzyme-linked immunosorbent assay (ELISA) kit test. Two quantitative structure-activity relationship (QSAR) techniques, regression analysis and comparative molecular field analysis (CoMFA), were applied for predicting the CR of PAHs in this ELISA kit. Parabolic regression indicates that the CRs are significantly correlated with the logarithm of the partition coefficient for the octanol-water system (log K _ow) (r ² = 0.643, n = 23, P < 0.0001), suggesting that hydrophobic interactions play an important role in the antigen-antibody binding and the cross-reactions in this ELISA test. The CoMFA model obtained shows that the CRs of the PAHs are correlated with the 3D structure of the molecules (r _cv ² = 0.663, r  ² = 0.873, F _4,32 = 55.086). The contributions of the steric and electrostatic fields to CR were 40.4 and 59.6%, respectively. Both of the QSAR models satisfactorily predict the CR in this PAH immunoassay kit, and help in understanding the mechanisms of antigen-antibody interaction.     

Prediction of retention data when using incremental multiple development techniques

Summary The apparentRF value of a compound after successive development steps in incremental multiple development (IMD) is determined. The model developed enables prediction of the migration and the zone width of investigated compounds in IMD with linearly and quadratically increasing development distances. For the experimental investigations we examined naturally occurring compounds as model substances on different stationary phases. The coincidence of predicted and measured chromatographic data strongly support our formulas. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis

When the generalized rank annihilation method (GRAM) is applied to liquid chromatographic data with diode-array detection, an important problem is the time shift of the peak of the analyte in the test sample. This problem leads to erroneous predictions. This time shift can be corrected if a time window is selected so that the chromatographic profile of the analyte in the test sample is trilinear with the peak of the analyte in the calibration sample. In this paper we present a new method to determine when this condition is met. This method is based on the curve resolution with iterative target transformation factor analysis (ITTFA). The calibration and test matrices are independently decomposed into profiles and spectra, and aligned before GRAM is applied. Here we study two situations: first, when the calibration matrix has one analyte and second, when it has two analytes. When the calibration matrix has two analytes, we selectively determine the time window for the analyte to be quantified. There were considerably fewer prediction errors after correction.     

Quantitative iterative target transformation factor analysis

Traditionally, improvement of the constrained alternating least squares (ALS) solution has been executed by the addition of a priori information in the initial estimates and or constraints. However, there are cases where this information simply does not exist or is impossible to acquire under the process conditions. Therefore, new strategies are required to produce starting estimates close to the actual solution without the need of a priori information. Quantitative iterative target transformation factor analysis (QITTFA) is developed as a solution to this problem. The QITTFA approach combines the strengths of both iterative target transformation factor analysis (ITTFA) and simple‐to‐use interactive self‐modelling mixture analysis (SIMPLISMA) to (1) produce a solution space spanned by the independent factors such that the variance contribution due to noise is reduced, (2) to iteratively refine the solutions space prior to ALS and (3) to select the most pure variables from the refined solution space using the purity criterion. It has been observed that the QITTFA approach markedly improves the conventional SIMPLISMA and second derivative SIMPLISMA performance in the presence and absence of selectivity. In addition, components of differing spectral characteristics (narrow or broad spectral features) can be resolved, without a priori knowledge of the shapes of the pure components. This has been demonstrated with a simulated high performance liquid chromatography‐diode array detection (HPLC‐DAD) dataset, a laboratory‐based UV–Vis calibration dataset and a gaseous near infrared (NIR) dataset from an industrial process. Copyright © 2007 John Wiley & Sons, Ltd.     

Peptide retention prediction applied to proteomic data analysis

A retention prediction model was developed for peptides separated in reversed-phase chromatography. The model was utilized to identify and exclude the false positive (FP) peptide identifications obtained via database search. The selected database included human proteins, as well as decoy sequences of random proteins. The FP peptide detection rate was defined either as number of retention time outliers, or random decoy sequence identifications. The FP rate for various MASCOT scores was calculated. The peptides identified in one-dimensional (1D) and two-dimensional (2D) liquid chromatography/mass spectrometry (LC/MS) experiments were validated by prediction models. Multi-dimensional LC was based on two orthogonal reversed-phase chromatography modes; prediction models were successfully applied for data filtering in both separation dimensions.     

Predicting retention data using the slope of the log adjusted retention time vs. carbon number plot for n-alkanes

Summary The slope of the n-alkane log plot dt′_R/dn_c (t′_R=adjusted retention time; n_c=carbon number) for a stationary phase can be used to obtain the retention index of an unidentified substance in a chromatogram containing only one peak with a known retention index, or to predict the retention time of a substance from that of a different homolog in the same series. It can also be used to translate retention indices into relative retention time, partition coefficient or specific retention volume. Published values of the slope are collected and critically evaluated. Equations are deduced that predict its approximate value at a specified temperature given the value at only one other temperature.     

Simultaneous polarographic analysis of pyrazine and its methyl derivatives by iterative target transformation factor analysis

The polarographic waves of pyrazine and its methyl derivatives are seriously overlapping, so they cannot be determined individually by polarographic methods without a prior separation. In this paper, a chemometric approach, iterative target transformation factor analysis (ITTFA), is developed and applied to the determination of mixtures of pyrazines at trace level (2.0–9.0 × 10⁻⁶moll⁻¹) by using differential pulse polarography (DPP) and a static mercury drop electrode (SMDE). Different from the general ITTFA method, only one-dimensional measurement data of n − 1 standards and an unknown were used in this work. It produced acceptable results with average recoveries in the 96–108% range and relative standard errors in the 3.4–9.5% range.     

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics: comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.     

A program for evaluating equilibrium constants from spectrophotometric data by non-linear regression analysis

A new program, CFTSP, is described for computing stability constants and molar absorptivities from data on the absorbances of mixtures of a metal ion with a ligand. It is written in FORTRAN 77, can run on personal computers, and has facilities for interactive data analysis and presentation that ease the operator's task in searching for the equilibrium model that best fits the experimental data. A critical evaluation of the performance of the program is presented, and some general criteria for selecting equilibrium parameters, making use of both synthetic and experimental data, are described.     

Binding of caffeic acid to human serum albumin by the retention data and frontal analysis

A new mathematical model and frontal analysis were used to characterize the binding behavior of caffeic acid to human serum albumin (HSA) based on high‐performance affinity chromatography. The experiments were carried out by injecting various mole amounts of the drug onto an immobilized HSA column. They indicated that caffeic acid has only one type of binding site to HSA on which the association constant was 2.75 × 10⁴/m . The number of the binding site involving the interaction between caffeic acid and HSA was 69 nm . The data obtained by the frontal analysis appeared to present the same results for both the association constant and the number of binding sites. This new model based on the relationship between the mole amounts of injection and capacity factors assists understanding of drug–protein interaction. The proposed model also has the advantages of ligand saving and rapid operation. Copyright © 2014 John Wiley & Sons, Ltd.     

目标转换渐进因子分析法研究化学平衡体系

本文提出了一种计算化学平衡常数的方法-目标转换渐进因子分析。该方法将新近发展起来的渐进因子分析方法与目标转换技术相结合, 它不仅可以给出体系的因子数目, 而且可以给出各因子的分布趋势。利用该法成功地测定了分析试剂溴邻苯三酚红的逐级解离常数, 结果与文献值吻合。     

The thermodynamic dissociation constant of naphazoline by the regression analysis of potentiometric data

The mixed dissociation constant of naphazoline is determined at various ionic strengths I [mol dm⁻³] in the range of 0.01 to 0.26 and at temperatures of 25°C and 37°C using ESAB and HYPERQUAD regression analysis of the potentiometric titration data. A strategy of efficient experimentation is proposed in a protonation constant determination, followed by a computational strategy for the chemical model with a protonation constant determination. Two group parameters, L ₀ and H _T were ill-conditioned in the model and their determination is therefore uncertain. These group parameters, L ₀ and H _T, can significantly influence a systematic error in the estimated common parameter pK_a and they always should be refined together with pK _a. The thermodynamic dissociation constant pK _a^T was estimated by nonlinear regression of {pK _a, I} data at 25°C and 37°C: for naphazoline pK _al^T = 10.41(1) and 10.13(2). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates to be found.      

Thermodynamic dissociation constants of isocaine, physostigmine and pilocarpine by regression analysis of potentiometric data

Concentration and mixed dissociation constant(s) of three drug acids, H(J)L, isocaine, physostigmine and pilocarpine, at various ionic strengths, I, in the range 0.03-0.81 and 25 degrees C have been determined with the use of regression analysis of potentiometric titration data when common parameter, pK(a), and group parameters E'(0), L(0), and H(T) are simultaneously refined. Internal calibration of the glass electrode cell in the concentration scale [H(+)] performed during titration was used. The estimate of ill-conditioned group parameters has a great influence on a systematic error in estimated pK(a) and therefore it makes the computational strategy important. As more group parameters are refined and a better fit achieved, a more reliable estimate of dissociation constants results. The thermodynamic dissociation constant, pK(a)(T), an ill-conditioned ion-size parameter, ?, and the salting-out coefficient, C, were estimated by non-linear regression of {pK(a), I} data and an extended Debye-Hückel equation. The goodness-of-fit test based on regression diagnostics is a measure of the reliability of parameters, and proves that reliable estimates for isocaine pK(a)(T)(=)8.96(1), ?=8(3) A and C=0.50(3) at 25 degrees C, for physostigmine pK(a)(T)(=)8.07(3), ?=19(26) A and C=0.64(3) at 25 degrees C, and for pilocarpine pK(a)(T)(=)7.00(1), ?=7(1) A and C=0.53(2) at 25 degrees C were found.     

Identification of noise in linear data sets by factor analysis

With the use of atomic and nuclear methods to analyze samples for a multitude of elements, very large data sets have been generated. Due to the ease of obtaining these results with computerized systems, the elemental data acquired are not always as thoroughly checked as they should be leading to some, if not many, bad data points. It is advantageous to have some feeling for the trouble spots in a data, set before it is used for further studies. A technique which has the ability to identify bad data points, after the data has been generated, is classical factor analysis. The ability of classical factor analysis to identify two different types of data errors make it ideally suited for scanning large data sets. Since the results, yielded by factor analysis indicate correlations between parameters, one must know something about the nature of the data set and the analytical techniques used to obtain it to confidentially isolate errors.